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we are trying to create a distribution that estimates pathogens presence on vegetables. This was done using different methods, each providing a distribution: - method S (from sludge concentration) is best fitted by weibull(1.55, 8.57) - method SO (from soil) is best fitted by logN(0.68, 0.63) - method F (from field data) PERT(0.093, 0.34, 0.52)

Theoretically the 3 methods should estimate the same value. What would be the best way to combine them?

I have searched online but I could only find & understand how to do it using normal distributions. The posterior normal distribution would have a mean that is a weighted average (see page 3 on https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading15a.pdf)

How to update different types of distributions?

Thank you for your help.

library(mc2d)
soil.df <- matrix(data=0, nrow=10000, ncol=3)
colnames(soil.df) <- c("from sludge","soil sample","field data")

for (i in 1:10000) {
  migration <- 0.27
  application <- rpert(1,0.01,0.02,0.25)
  C <- rweibull(1,1.57,85.79)
  soil.df[i,1] <- C*application*migration ##from sludge
  soil.df[i,2]<- 10^rnorm(1,0.68,0.63)*migration ## from soil concentration
  soil.df[i,3] <- rpert(1,0.093, 0.34, 0.52) ##from field data

}

par(mfrow=c(1,1))
plot(density(soil.df[,1]), col="red", xlim=c(0,15), ylim=c(0,1), main="Ova/gr soil")
lines(density(soil.df[,2]), col="black")
lines(density(soil.df[,3]), col="green")
StupidWolf
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G B
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  • Hi GB, so the formula you see works only for normal distribution. For other distribution, you have derive the posterior..and I really don't know how to do it. Might needa ask it in cross validated? – StupidWolf Nov 10 '19 at 13:30
  • thanks for your suggestion. I was wondering if there is a numerical solution, maybe using Monte Carlo... – G B Nov 10 '19 at 17:29

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